Answers:
Team A = 175 people
Team B = 150 people
This is before the 45 students transfer from A to B.
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Step-by-step explanation:
x = number of people in team A
y = number of people in team B
These counts are before the 45 pupils transfer from A to B.
The counts are in ratio 7:6, which means,
x/y = 7/6
6x = 7y
x = 7y/6
If we subtract 45 people from team A, we have x-45 people left. Those 45 people go to team B to have y+45 pupils there.
The quantities x-45 and y+45 are in ratio 2:3, so,
(x-45)/(y+45) = 2/3
3(x-45) = 2(y+45)
3x-135 = 2y+90
3(7y/6)-135 = 2y+90 .... plug in x = 7y/6
21y/6 - 135 = 2y+90
6*( 21y/6 - 135 ) = 6*(2y+90)
21y-810 = 12y+540
21y-12y = 540+810
9y = 1350
y = 1350/9
y = 150
x = 7y/6
x = 7(150)/6
x = 175
We have 175 people on team A, and 150 people on team B.
This is before the 45 students transfer from A to B.
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Check:
x/y = 175/150 = (7*25)/(6*50) = 7/6
This shows x and y are in ratio 7:6 to match the instructions.
x-45 = 175-45 = 130
y+45 = 150+45 = 195
(x-45)/(y+45) = 130/195 = (2*65)/(3*65) = 2/3
And we have the updated counts in the ratio 2:3, which matches the stated info in the instructions. The answers are fully confirmed.